Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+y &= -1 \\ -9x+2y &= -1\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-9x = -2y-1$ Divide both sides by $-9$ to isolate $x$ $x = {\dfrac{2}{9}y + \dfrac{1}{9}}$ Substitute this expression for $x$ in the first equation. $-7({\dfrac{2}{9}y + \dfrac{1}{9}}) + y = -1$ $-\dfrac{14}{9}y - \dfrac{7}{9} + y = -1$ Simplify by combining terms, then solve for $y$ $-\dfrac{5}{9}y - \dfrac{7}{9} = -1$ $-\dfrac{5}{9}y = -\dfrac{2}{9}$ $y = \dfrac{2}{5}$ Substitute $\dfrac{2}{5}$ for $y$ in the top equation. $-7x+ \dfrac{2}{5} = -1$ $-7x+\dfrac{2}{5} = -1$ $-7x = -\dfrac{7}{5}$ $x = \dfrac{1}{5}$ The solution is $\enspace x = \dfrac{1}{5}, \enspace y = \dfrac{2}{5}$.